Single Bottleneck Research Articles

Dimensioning bandwidth for elastic traffic in high-speed data networks

Simple and robust engineering rules for dimensioning bandwidth for elastic data traffic are derived for a single bottleneck link via normal approximations for a closed-queueing network (CQN) model in heavy traffic. Elastic data applications adapt to available bandwidth via a feedback control such as the transmission control protocol (TCP) or the available bit rate transfer capability in asynchronous transfer mode. The dimensioning rules satisfy a performance objective based on the mean or tail probability of the per-flow bandwidth. For the mean objective, we obtain a simple expression for the effective bandwidth of an elastic source. We provide a new derivation of the normal approximation in CQNs using more accurate asymptotic expansions and give an explicit estimate of the error in the normal approximation. A CQN model was chosen to obtain the desirable property that the results depend on the distribution of the file sizes only via the mean, and not the heavy-tail characteristics. We view the exogenous "load" in terms of the file sizes and consider the resulting flow of packets as dependent on the presence of other flows and the closed-loop controls. We compare the model with simulations, examine the accuracy of the asymptotic approximations, quantify the increase in bandwidth needed to satisfy the tail-probability performance objective as compared with the mean objective, and show regimes where statistical gain can and cannot be realized.

Limited diversity of peptides related to an alloreactive T cell epitope in the HLA-B27-bound peptide repertoire results from restrictions at multiple steps along the processing-loading pathway.

The influence of various factors along the processing-loading pathway in limiting the diversity of HLA-B27-bound peptides around a core protein sequence was analyzed. The C5 proteasome subunit-derived RRFFPYYV and RRFFPYYVY peptides are natural B*2705 ligands. The octamer is an allospecific CTL epitope. Digestion of a 27-mer fragment of C5 revealed that both ligands are generated from this precursor substrate with the 20S proteasome in vitro in a ratio comparable to that in the B*2705-bound peptide pool. The C5 sequence allowed to derive a nested set of six additional peptides with 8-11 residues containing the core octamer sequence and the Arg2 motif of HLA-B27, none of which was found in the B27-bound pool. Together, low proteasomal yield, disfavored TAP-binding motifs, and low affinity for B*2705 accounted for the absence of four of the six peptides. The two remaining differed from the natural octamer or nonamer ligands only by an additional N-terminal Ser residue. Their stability in complex with B*2705 was lower than the respective natural ligands, raising the possibility that N-terminal trimming might have favored a shift toward the more stable peptides. The results suggest that the B*2705-bound peptide repertoire has a highly restricted diversity around a core alloantigenic sequence. This is not explained by a single bottleneck feature, but by multiple factors, including proteasomal generation, TAP-binding motifs, MHC-binding efficiency, and perhaps optimized stability through N-terminal trimming. Tapasin-dependent restrictions, although not excluded, were not required to explain the absence in vivo of the particular peptide set in this study.

Performance analysis of data packet discarding in ATM networks

Data performance in ATM networks should be measured on the packet level instead of the cell level, since one or more cell losses within each packet is equivalent to the loss of the packet itself. Two packet-level control schemes, packet tail discarding and early packet discarding, were proposed to improve data performance. In this paper, a new stochastic modeling technique is developed for performance evaluation of two existing packet-discarding schemes at a single bottleneck node. We assume that the data arrival process is independent of the nodal congestion, which may represent the unspecified bit-rate traffic class in ATM networks, where no end-to-end feedback control mechanism is implemented. Through numerical study, we explore the effects of buffer capacity, control threshold, packet size, source access rate, underlying high-priority real-time traffic, and loading factor on data performance, and discuss their design tradeoffs. Our study shows that a network system can he entirely shut down in an overload period if no packet-discarding control scheme is implemented, under the assumption that there are no higher layer congestion avoidance schemes. Further, unless with sufficiently large buffer capacity, early packet discarding (EPD) always outperforms packet tail discarding (PTD) significantly under most renditions. Especially under the overload condition, EPD can always achieve about 100% goodput and 0% badput, whereas the PTD performance deteriorates rapidly. Among all the factors, the packet size has a dominant impact on EPD performance. The optimal selection of the EPD queue control threshold to achieve the maximum goodput is found to be relatively insensitive to traffic statistics.

Optimal Dispersion of Morning Commuters in Road Networks with Queueing

The purpose of this study is to derive an optimal distribution of work start times (W-curve) that effectively minimizes the social cost for morning commuters in road networks with queuing. Specifically, we consider the following bi-level programming problem: the lower-level problem describes equilibrium flow patterns under a given W-curve, and the upper-level problem optimizes a W-curve under the equilibrium constraints. We first derive the optimal W-curve for a basic model where homogeneous commuters pass through a single bottleneck. We then extend the analysis to the case where both route choice and departure time choice are simultaneously determined.

Stability and performance analysis of rate-based feedback flow controlled ATM networks

Motivated by the ABR class of service in ATM networks, we study a continuous-time queueing system with a feedback control of the arrival rate of some of the sources. The feedback regarding the queue length or the total workload is provided at regular intervals (variations on it, especially the EPRCA algorithm, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single bottleneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing the continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow, and lower delay jitter than any open-loop policy.

An empirical study of TCP/IP performance over ATM

This paper outlines some basic performance characteristics of the Transmission Control Protocol/Internet Protocol (TCP/IP) over Asynchronous Transfer Mode (ATM). It also discusses a few solutions to assure acceptable TCP/IP performance over ATM which are implemented by the industry during the last couple of years. The conclusions in this paper are based on empirical TCP/IP performance test results collected on a DS3 ATM research testbed, architected with commercially available IP and ATM equipment 2 This paper does not endorse any specific equipment. Tests were performed with available equipment in the lab. 2 . TCP/IP performance can vary widely and suffer significantly over ATM networks with large bandwidth*delay products. First, it is essential that the TCP window size matches the bandwidth*delay product of the end-to-end connection to fully utilize the bandwidth provided by the broadband network. Even if the window size meets this criteria, TCP performance can still be unacceptable, especially if the buffering within the ATM network is limited. A single limited-buffer bottleneck is sufficient to degrade the performance of a TCP connection when multiple traffic sources congest the bottleneck resource, such as in ATM networks with small buffer switches. One approach to assure acceptable TCP/IP performance is to limit the data rate into the bottleneck resource by exercising rate control at the entry to the ATM network. A better solution is to provide sufficient buffering within the ATM network.

The conceptual structure of traffic jams

Area-wide traffic jams develop through the propagation of queues from link to link, a process that resembles the growth of branches on a tree. The process is not well understood. In this paper, simple models for jam growth arising from a single bottleneck are developed for an idealized grid network. Under these idealized conditions, it has been shown that there are essentially two possible spatial configurations for a traffic jam on the type of network considered, each having a characteristic form sharing some of the properties of a fractal. More important, the models highlight an interesting dilemma in traffic management. A strategy that aims to minimize the rate of growth of a jam by a suitable allocation of queue storage space will actually encourage gridlock at the heart of the congested area, and conversely, a strategy that aims to defer gridlock will result in queues spread over a wider area. Extensive channelization (normally advocated in the interests of efficient traffic flow and safety) will also encourage longer queues. With hindsight, these conclusions seem obvious for any network whether imaginary or real, but they do not seem to have appeared in the literature, and the models give some indication of the size of the effects involved.

Production scheduling of single-stage multi-product batch chemical processes with fixed batch sizes

We address the problem of scheduling a single-stage multi-product batch chemical process with fixed batch sizes. We present a mixed-integer nonlinear programming model to determine the schedule of batches, the batch size, and the number of overtime shifts that satisfy the demand at minimum cost for this process. We introduce a polynomial-time algorithm to solve the problem when the processing times of all batches are identical and the setup and cleaning times are sequence-independent. The solution procedure is based on recognizing that the optimal fixed batch size is a member of a set whose cardinality is polynomial. Given a batch size, the problem may be formulated as an assignment problem. Thus, an optimal solution may be found by iteratively solving a polynomial number of assignment problems. This work was motivated by a pesticide manufacturing company in the design of a new plant where the assumptions of a single bottleneck machine, fixed batch sizes, sequence-independent setup times, and identical batch processing times are all valid. An example is developed for this application.

Production scheduling of single-stage multi-product batch chemical processes with fixed batch sizes

We address the problem of scheduling a single-stage multi-product batch chemical process with fixed batch sizes. We present a mixed-integer nonlinear programming model to determine the schedule of batches, the batch size, and the number of overtime shifts that satisfy the demand at minimum cost for this process. We introduce a polynomial-time algorithm to solve the problem when the processing times of all batches are identical and the setup and cleaning times are sequence-independent. The solution procedure is based on recognizing that the optimal fixed batch size is a member of a set whose cardinality is polynomial. Given a batch size, the problem may be formulated as an assignment problem. Thus, an optimal solution may be found by iteratively solving a polynomial number of assignment problems. This work was motivated by a pesticide manufacturing company in the design of a new plant where the assumptions of a single bottleneck machine, fixed batch sizes, sequence-independent setup times, and identical batch processing times are all valid. An example is developed for this application.

An extension to the single bottleneck transportation problem

Abstract In the existing models of bottleneck transportation problem (BTP), the transport time along a given path is taken as a fixed charge. In most practical situations, however, the transport time usually varies with the amount of transport. In order to make up this defect, an extended BTP model is built in which transport time tij is determined by a function of the amount to be transported rather than a constant. A heuristic recursive algorithm is proposed for the solution of the model. Furthermore, a special case of the model (that the supplies at sources are sufficient) is studied and a set of formulae of optimal solution are derived.

Allocation of buffers to serial production lines with bottlenecks

The optimal placement of a predetermined amount of buffer capacity in balanced serial production lines is a well-understood problem: in lines with moderate variability, the optimal allocation involves equal numbers of buffers at each site; in lines with severe variability, the equal allocation is modified slightly to place more buffers toward the center of the line. Buffering unbalanced lines is a much less well-understood problem. We study the problem of buffering serial lines with moderate variability and a single bottleneck; i.e., a single station with a larger mean processing time than all other stations. Our analysis shows that a bottleneck station draws buffers toward it, but the optimal allocation depends on the location and severity of the bottleneck, as well as the number of buffers available. Furthermore, relatively large imbalances in mean processing times are required to shift the optimal buffer allocation away from an equal allocation. Finally, line length appears to have a relatively small e...

Single bottleneck systems with proportional expected yields and rigid demand

This study considers single bottleneck systems: multistage production systems where all setup costs except one are zero. The stage with non-zero setup cost is defined to be the bottleneck (BN). Production is in lots and demand needs to be satisfied in its entirety. The expected yield (number of good units) at each stage is proportional to the lot size and only good items may proceed from one stage to another. We reveal several general features of the optimal policy and discuss some specific yields in detail. In particular it is shown that if units are processed one-by-one on the non-BNs, the optimal lotsizing problem can be reduced to the problem of optimally lotsizing a single-stage ‘equivalent machine’. Then, if the BN has Binomial yeild, the ‘equivalent machine’ itself has Binomial yields. Also, examples are given which demonstrate the non-intuitive structure of the optimal policy.

Feedback-based flow control of B-ISDN/ATM networks

We consider a system comprising of a single bottleneck switch/node that is fed by N independent Markov-modulated fluid sources. There is a fixed propagation delay incurred by the traffic between these sources and the switch. We assume that the switch sends periodic feedback in the form of a single congestion indicator bit. This feedback also incurs a fixed propagation delay in reaching the sources. Upon reaching the sources (or the access controllers associated with the sources), this congestion indicator bit is used to choose between two rates for the excess traffic, high or low, possibly depending on the state of that source. The switch employs a threshold mechanism based on its buffer level to discard excess traffic. We show that the stationary distribution of this system satisfies a set of first-order linear differential equations along with a set of split boundary conditions. We obtain an explicit solution to these using spectral decomposition. To this end we investigate the related eigenvalue problem. Based on these results we investigate the role of delayed feedback vis-a-vis various time-constants and traffic parameters associated with the system. In particular, we identify conditions under which the feedback scheme offers significant improvement over the open-loop scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Applying an Architecture for General Intelligence to Reduce Scheduling Effort

A system called Merle-Soar is described which demonstrates how a specific architecture for general intelligence and learning (Soar) can be used to reduce scheduling effort when solving simple scheduling problems. In particular, we describe how Merle-Soar schedules sequences of jobs on a single bottleneck machine in a job shop. The knowledge of dispatching, acquired from examining how a human expert performs the task, is cast as search rules. A study was conducted which examined the extent to which learning could contribute to decreases in scheduling effort; specifically, the contribution of learning within-tasks was explored—the change in reasoning effort while solving a particular scheduling problem as knowledge is accumulated from successive trials. The results indicated that dramatic reductions in scheduling effort (in terms of the Soar architecture) were obtained. Knowledge gained early in the scheduling task was subsequently applied later in the task to reduce deliberation, and knowledge gained from one trial successfully reduced deliberation effort in subsequent trials. Additionally, the reduction exhibited the general power law of learning documented in psychological studies of skill acquisition. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

A Single Bottleneck System with Binomial Yields and Rigid Demand

This paper considers a “single bottleneck system”: a multistage production system where all setups except one are zero. The stage with nonzero setup is defined to be the bottleneck; it may be thought of as the critical resource whose throughput largely determines the throughput of the entire system, as a envisioned by the OPT philosophy. Production is in lots with uncertain (binomial) yields and demand needs to be satisfied in full, thus possibly necessitating multiple production runs. We show how the optimal control problem can be reduced to that of optimal lotsizing a single stage.

A comparison of two lot sizing-sequencing heuristics for the process industry

Two heuristics for operational production planning in a chemical processing environment are compared, characterized by a single bottleneck machine, fixed batch sizes, sequence-dependent setup-times, as well as production and storage constraints. Performance of both heuristics is measured by means of simulation experiments in which the planning horizon is partially frozen and rolled a number of times, as would be the case in practical applications. Furthermore, demand uncertainty is simulated as well as the variability among setup times. The performance measure used is the total cost for executing a particular production plan over its entire planning horizon.

Half a century of research on the Stroop effect: An integrative review.

The literature on interference in the Stroop Color-Word Task, covering over 50 years and some 400 studies, is organized and reviewed. In so doing, a set of 18 reliable empirical finding is isolated that must be captured by any successful theory of the Stroop effect. Existing theoretical positions are summarized and evaluated in view of this critical evidence and the 2 major candidate theories ―relative speed of processing and automaticity of reading― are found to be wanting. It is concluded that recent theories placing the explanatory weight on parallel processing of the irrelevant and the relevant dimensions are likely to be more sucessful than are earlier theories attempting to locate a single bottleneck in attention

A network of priority queues in heavy traffic: One bottleneck station

In this paper we consider an open queueing network having multiple classes, priorities, and general service time distributions. In the case where there is a single bottleneck station we conjecture that normalized queue length and sojourn time processes converge, in the heavy traffic limit, to one-dimensional reflected Brownian motion, and present expressions for its drift and variance. The conjecture is motivated by known heavy traffic limit theorems for some special cases of the general model, and some conjectured “Heavy Traffic Principles” derived from them. Using the known stationary distribution of one-dimensional reflected Brownian motion, we present expressions for the heavy traffic limit of stationary queue length and sojourn time distributions and moments. For systems with Markov routing we are able to explicitly calculate the limits.

Asymptotically exact decomposition approximations for open queueing networks

Two decomposition approximations are presented for mean sojourn times in open single class queueing networks. If there is a single bottleneck station, the approximations are asymptotically exact in both light and heavy traffic. When applied to a Jackson network or an M/G/1 queue, these approximations are exact for all values of the traffic intensity. They also perform reasonably well on some small examples.

Some observations on the dynamics of a congestion control algorithm

We use simulation to make some observations about the behavior of the congestion control algorithm currently embedded in the 4.3-Tahoe BSD TCP implementation. We investigate a simple case of a few TCP connections, originating and terminating at the same pair of hosts, using a single bottleneck link. Our simulations reveal two unexpected phenomena. First, packets from the individual connections, rather than being mixed together, completely separate into individual clusters. Second, every connection loses a single packet during each congestion epoch. As a way of exploring the cause of these phenomena, we discuss how the behavior is altered by modifications to the congestion control algorithm and to the switch queue control algorithm .